IM Geo.3.11 Lesson: Splitting Triangle Sides with Dilation, Part 2

What do you notice? What do you wonder?
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[/img]
Does a line parallel to one side of a triangle always create similar triangles?
Create several examples. Decide if the conjecture is true or false. If it’s false, make a more specific true conjecture.[br]
Find any additional information you can be sure is true.[br]Label it on the diagram below.
Write an argument that would convince a skeptic that your conjecture is true.[br]
Find the length of each unlabelled side.
Segments [math]AB[/math] and [math]EF[/math] are parallel.
Find the length of each unlabelled side.
Segments [math]BD[/math] and [math]FG[/math] are parallel. Segment [math]EG[/math] is 12 units long. Segment [math]EB[/math] is 2.5 units long.
Find the lengths of sides [math]CE[/math], [math]CB[/math], and [math]CA[/math] in terms of [math]x[/math], [math]y[/math], and [math]z[/math] in the applet below. Explain or show your reasoning.
Cerrar

Información: IM Geo.3.11 Lesson: Splitting Triangle Sides with Dilation, Part 2